multiple - choice 10 points\nethan is studying the weights, measured in pounds, of pumpkins grown at two…

multiple - choice 10 points\nethan is studying the weights, measured in pounds, of pumpkins grown at two different farms. the boxplots show the distribution of pumpkin weight for two samples of equal size, one from farm a and the other from farm b.\nfarm a\nfarm b\n6 8 10 12 14 16 18 20 22\npumpkin weight (pounds)\nbased on the boxplots, which of the following is a correct conclusion about the distribution of pumpkin weight for the samples from the two farms?\nthere are more pumpkin weights that are less than pounds from farm b than there are from farm a.\nthe range of the pumpkin weights for farm b is greater than the range for farm a.\nthere are more pumpkin weights that are greater than pounds from farm a than there are from farm b.\nthere are more pumpkin weights that are greater than pounds from farm b than there are from farm a.\nthe interquartile ranges of the pumpkin weights are the same for farm a and farm b.

multiple - choice 10 points\nethan is studying the weights, measured in pounds, of pumpkins grown at two different farms. the boxplots show the distribution of pumpkin weight for two samples of equal size, one from farm a and the other from farm b.\nfarm a\nfarm b\n6 8 10 12 14 16 18 20 22\npumpkin weight (pounds)\nbased on the boxplots, which of the following is a correct conclusion about the distribution of pumpkin weight for the samples from the two farms?\nthere are more pumpkin weights that are less than pounds from farm b than there are from farm a.\nthe range of the pumpkin weights for farm b is greater than the range for farm a.\nthere are more pumpkin weights that are greater than pounds from farm a than there are from farm b.\nthere are more pumpkin weights that are greater than pounds from farm b than there are from farm a.\nthe interquartile ranges of the pumpkin weights are the same for farm a and farm b.

Answer

Explanation:

Step1: Recall box - plot concepts

A box - plot shows the five - number summary (minimum, first quartile (Q_1), median (Q_2), third quartile (Q_3), maximum). The range is (R=\text{Max}-\text{Min}) and the inter - quartile range is (IQR = Q_3 - Q_1).

Step2: Analyze range

For Farm A: The minimum is around 6 and the maximum is around 22, so the range (R_A=22 - 6=16). For Farm B: The minimum is around 8 and the maximum is around 20, so the range (R_B=20 - 8 = 12). So the range of Farm A is greater than that of Farm B.

Step3: Analyze inter - quartile range

The length of the box in a box - plot represents the inter - quartile range. The length of the box for Farm A and Farm B appears to be the same. Let's assume (Q_1) and (Q_3) values for Farm A are (Q_{1A}), (Q_{3A}) and for Farm B are (Q_{1B}), (Q_{3B}). Since the box lengths (Q_{3A}-Q_{1A}=Q_{3B}-Q_{1B}), the inter - quartile ranges are the same.

Step4: Analyze number of values less or greater than a certain value

We cannot determine the exact number of values less or greater than a certain value just from the box - plot as it does not show the frequency distribution within each part of the box - plot.

Answer:

The interquartile ranges of the pumpkin weights are the same for farm A and farm B.